Let's break this down. We're going to add 2819 and 9779 together.

Step 1: We'll start by adding the digits 9 & 9 in column 1 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 1 & 7 in column 2 and get 9.

Step 3: We'll start by adding the digits 8 & 7 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 2 & 9 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 2819 + 9779 = 12598.

